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Minimum Degree and Disjoint Cycles in Claw-Free Graphs

Published online by Cambridge University Press:  02 February 2012

RALPH J. FAUDREE ,
RONALD J. GOULD  and
MICHAEL S. JACOBSON
RALPH J. FAUDREE
Affiliation:
University of Memphis, Memphis, TN 38152, USA (e-mail: rfaudree@memphis.edu)
RONALD J. GOULD
Affiliation:
Emory University, Atlanta, GA 30322, USA (e-mail: rg@mathcs.emory.edu)
MICHAEL S. JACOBSON
Affiliation:
University of Colorado Denver, Denver, CO 80217, USA (e-mail: Michael.Jacobson@ucdenver.edu)
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Abstract

A graph is claw-free if it does not contain an induced subgraph isomorphic to K1,3. Cycles in claw-free graphs have been well studied. In this paper we extend results on disjoint cycles in claw-free graphs satisfying certain minimum degree conditions. In particular, we prove that if G is claw-free of sufficiently large order n = 3k with δ(G) ≥ n/2, then G contains k disjoint triangles.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 21 , Issue 1-2: Honouring the Memory of Richard H. Schelp , March 2012 , pp. 129 - 139
Copyright
Copyright © Cambridge University Press 2012

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References

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